Universal correlators for multi-arc complex matrix models

TL;DR

This paper demonstrates the universality of correlation functions in multi-arc complex matrix models across different eigenvalue supports, extending known results and providing explicit multi-loop correlator calculations.

Contribution

It introduces an iterative method to solve loop equations for multi-arc complex matrix models, establishing universality classes and explicit genus-one correlator results.

Findings

Universality of correlation functions across multi-arc models.

Explicit genus-one correlator formulas for any number of arcs.

Detailed analysis of the two-arc case and double-scaling limit.

Abstract

The correlation functions of the multi-arc complex matrix model are shown to be universal for any finite number of arcs. The universality classes are characterized by the support of the eigenvalue density and are conjectured to fall into the same classes as the ones recently found for the hermitian model. This is explicitly shown to be true for the case of two arcs, apart from the known result for one arc. The basic tool is the iterative solution of the loop equation for the complex matrix model with multiple arcs, which provides all multi-loop correlators up to an arbitrary genus. Explicit results for genus one are given for any number of arcs. The two-arc solution is investigated in detail, including the double-scaling limit. In addition universal expressions for the string susceptibility are given for both the complex and hermitian model.